Recently, quantum phases of matter have been studied which are characterized by fractionalized quasiparticles of the same type of spin liquids and fractional quantum Hall systems [1]}, [2]}, [3]}, [4]}, [5]}, which are commonly described in terms of gauge theories [6]}, [7]}, [8]}. But, differently from the latter, these new 4D phases are described by higher rank symmetric tensor fields, rather than vectors [9]}, [10]}, [11]}, [12]}, [13]}. The corresponding fractionalized quasiparticles have been called “fractons”, which are excitations of \(U(1)\)  gauge field theories which generalize the usual electromagnetism. The defining property of these quasiparticles is their complete or partial immobility [14]}, [15]}, [16]}. This property may be achieved through an extension of the usual electromagnetic theory, where the spatial vector gauge field \(A_i\)  is substituted by a rank-2 spatial symmetric tensor gauge field \(A_{ij}\) . Now, the usual gauge symmetry
\(\delta A_i=\partial _i\Phi \) 
